Question

Adobe Acrobat Reader DC Help 8.4.pdf 8.5.pdf TanFin 10_Appendix. final review.pdf Final Exa 5 76 100% 6. There are 5 red balls and 7 blue balls in an urn. Two balls are drawn consecutively without replacement. What is the probability that the first ball drawn is red given that the second ball drawn is also red?

Answer 1

There are 12 balls in an urn of which 5 are red and 7 are blue. 2 balls are drawn without replacement. Let A be the event that the first ball drawn is red and B be the event that the second ball drawn is red. It is required to find the probability P(A|B).

now, P(A)=5/12

Probabilty that the second ball is red consists of 2 situations. (i) first ball drawn is red, second ball drawn is also red and (ii) first ball drawn is blue but the second ball drawn is red.

Hence, P(B) = (5/12)*(4/11) + (7/12)*(5/11) = 55/132

A ∩ B means both A & B are red. Hence, P(A∩B) = (5/12)*(4/11) = 20/132

Hence, P(A|B)=P(A∩B)/P(B) = (20/132)/(55/132) = 20/55 = 4/11

answer is 4/11